【下载】Generalized Linear Models：A Bayesian Perspective~Dipak K. Dey.2000

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Generalized Linear Models: A Bayesian Perspective (Chapman & Hall/CRC Biostatistics Series) (Hardcover)
Dipak K. Dey (Editor), Sujit K. Ghosh (Editor), Bani K. Mallick (Editor)

Editorial Reviews
Review
"…both accessible and valuable." -- Statistical Methods in Medical Research
Product Description
Describes how to perform, conceptualize, and critique traditional generalized linear models from a Bayesian perspective and how to use modern computational methods to summarize inferences using simulation. DLC: Linear models (Statistics).

Product Details

• Hardcover: 440 pages
• Publisher: CRC Press; 1 edition (May 25, 2000)
• Language: English
• ISBN-10: 0824790340
• ISBN-13: 978-0824790349

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关键词：Generalized perspective Generalize Perspectiv Bayesian accessible summarize methods Series

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Contents
I General Overview 1
1 Generalized Linear Models: A Bayesian View 3
A. Gelfand & M. Ghosh
1. Introduction 3
2. GLMs and Bayesian Models 4
2.1 GLMs 4
2.2 Bayesian Models 5
3. Propriety of Posteriors 8
4. Semiparametric GLMs 10
5. Overdispersed Generalized Linear Models 12
6. Model Determination Approaches 14
2 Random Effects in Generalized Linear Mixed Models (GLMMs) 23
D. Sun, P. L. Speckman & R. K. Tsutakawa
1. Introduction 23
2. The Model 24
3. Random Effects 26
3.1 Independent Random Effects 26
3.2 Correlated Random Effects 26
3.3 Strongly Correlated Random Effects 29
3.4 Some Examples of the AR(d) Model 31
4. Hierarchical GLMMs 31
5. Bayesian Computation 36
3 Prior Elicitation and Variable Selection for Generalized Linear Mixed Models 41
J. Ibrahim & M. И. Chen
1. Introduction 41
2. Generalized Linear Mixed Models 43
2.1 Models 43
2.2 The Prior Distributions 44
2.3 Propriety of the Prior Distribution 46
2.4 Specifying the Hyperparameters 47
2.5 The Posterior Distribution and its Computation ....... 48
3. Bayesian Variable Selection 48
4. Pediatric Pain Data 51
5. Discussion 52
II Extending the GLMs 55
4 Dynamic Generalized Linear Models 57
M. A. R. Ferreira & D. Gamerman
1. Introduction 57
2. Dynamic linear models . 58
3. Definition and first approaches to inference .............. 59
3.1 Linear Bayes Approach 60
3.2 Piecewise Linear Approximation 61
3.3 Posterior Mode Estimation . 61
3.4 Other Approaches and Models 62
4. MCMC-based Approaches 62
4.1 Gibbs Sampling 63
4.2 Metropolis-Hasting Algorithm 64
5. Applications 65
5.1 Application 1: Meningococcic Meningitis 6d>
5.2 Application 2: Respiratory Diseases and Level of Pollutants . 68
6. Discussions and Extensions 70
5 Bayesian Approaches for Overdispersion in Generalized Linear Mod- els 73
D. K. Dey & N. Ravishanker
1. Introduction 73
2. Classes of Overdispersed General Linear Models 75
3. Fitting OGLM in the Parametric Bayesian Framework 78
3.1 Model Fitting 78
3.2 Example: Overdispersed Poisson Regression Model 79
3.3 Model Determination for Parametric OGLM's 80
4. Modeling Overdispersion in the Nonparametric Bayesian Framework 81
4.1 Fitting DP Mixed GLM and OGLM 81
4.2 Example; Overdispersed Binomial Regression Model 83
4.3 Model Determination for Dirichlet Process Mixed Models . . 83
5. Overdispersion in Multistage GLM 84
6 Bayesian Generalized Linear Models for Inference About Small Areas 89
B. Nandram
1. Introduction 89
2. Logistic Regression Models 91
3. Poisson Regression Models 94
4. Computational Issues 96
5. Models for the U.S. Mortality Data 100
6. Challenges in Small Area Estimation 102
7. Concluding Remarks 104

III Categorical and Longitudinal Data 111
7 Bayesian Methods for Correlated Binary Data 113
S. Chib
1. Introduction 113
2. The Multivariate Probit Model 114
2.1 Dependence Structures 116
2.2 Student-t Specification 116
2.3 Estimation of the MVP Model 117
2.4 Fitting of the Multivariate t-link Model 118
3. Longitudinal Binary Data 119
3.1 Probit (or logit) Normal Model 119
3.2 Inference 120
3.3 Computations for the Probit-Normal Model 120
3.4 Binary Response Hierarchical Model 122
3.5 Other Models 123
4. Comparison of Alternative Models 124
4.1 Likelihood Ordinate 124
4.2 Posterior Ordinate 125
5. Concluding Remarks 127
6. Appendix 127
6.1 Algorithm 1 127
6.2 Algorithm 2 128
6.3 Algorithm 3 129
8 Bayesian Analysis for Correlated Ordinal Data Models 133
M. ff. Chen & D. K. Dey
1. Introduction 133
2. Models 135
3. Prior Distributions and Posterior Computations 138
3.1 Prior Distributions 138
3.2 Posterior Computations 138
4. Model Determination 142
4.1 Model Comparisons 143
4.2 Model Diagnostics 146
5. Item Response Data Example 148
6. Concluding Remarks 155
9 Bayesian Methods for Time Series Count Data 159
J, Ibrahim & M. H. Chen
1. Introduction 159
2. The Method 160
2.1 The Likelihood Function 160
2.2 The Prior Distributions 162
2.3 Specifying the Hyperparameters 164
2.4 Prior Distribution on the Model Space 164
3. Computation of Model Probabilities 165
4. Example: Pollen Data 167
5. Discussion 168
10 Item Response Modeling 173
J. Albert & M. Ghosh
1. Introduction 173
2. An Item Response Curve 175
3. Administering an Exam to a Group of Students 176
4. Prior Distributions 178
4.1 Noninformative Priors and Propriety of the Posterior Distri- bution 178
4.2 Choosing an Informative Prior 180
5. Bayesian Fitting of Item Response Models 181
5.1 Fitting of the Two-parameter Model Using Gibbs Sampling . 181
5.2 Implementation of Gibbs Sampling for General F 183
5.3 Gibbs Sampling for a Probit Link Using Data Augmentation 184
5.4 Bayesian Fitting of the One-parameter Model ......... 185
6. Inferences from the Model ........................ 185
7. Model Checking .............................. 186
7.1 Bayesian Residuals . 186
7.2 Posterior Predictive Checks 187
8. The Mathematics Placement Test Example 188
9. Further Reading 191
11 Developing and Applying Medical Practice Guidelines Following Acute Myocardial infarction: A Case Study Using Bayesian Probit and Logit Models 195
M. B. Landrum & S. Normand
1. Background and Significance 195
2. Developing Practice Guidelines . 197
2.1 Elicitation of Appropriateness Ratings 197
2.2 Combining the Angiography Panel Data ............ 198
2.3 Estimation 199
2.4 Defining the Standard of Care 199
2.5 Results 200
3. Applying the Practice Guidelines 200
3.1 Study Population 200
3.2 Modeling Adherence to Practice Guidelines 202
3.3 Estimation 203
3.4 Profiling Hospitals 203
3.5 Explaining Variability in Quality of Care 204
3.6 Results 205
4. Discussion 209

IV Semiparametric Approaches 215
12 Semiparametric Generalized Linear Models: Bayesian Approaehes217
B. K. Mallick, D. G. T. Denison & A.F. M. Smith
1. Introduction 217
2. Modeling the Link Function g ...................... 218
2.1 Binary Response Regression 218
2.2 General Regression 219
3. Modeling the Systematic Part r) . . . 219
3.1 Model with Random Effects 220
3.2 Model with Deterministic Error ................. 220
4. Models Using Curves and Surfaces . 220
5. GLMs using Bayesian MARS ...................... 221
5.1 Classical MARS 221
5.2 Bayesian MARS 222
5.3 Bayesian MARS for GLMs 224
6. Examples of Bayesian MARS for GLMs 224
6.1 Motivating Example ....................... 224
6.2 Pima Indian Example 225
13 Binary Response Regression with Normal Scale Mixture Links 231
S. Basu & S. Mukhopadhyay
1. Introduction 231
2. The Finite Mixture Model 233
3. General Mixtures and a Dirichlet Process Prior 234
4. Model Diagnostic 236
4.1 Basic Goal 236
4.2 Diagnostic Tools 237
4.3 Computational Methods 237
5. Application: Student Retention at the University of Arkansas .... 237
6. Discussion . 239
14 Binary Regression Using Data Adaptive Robust Link Functions 243
R. Haro-Lopez, B. K, Mallick & A. F. M, Smiih
1. Introduction 243
2. The Binary Regression Model 244
3. Detection of Outliers and Model Comparison 248
4. Numerical Illustration . 248
5. Discussion 250
15 A Mixture-Model Approach to the Analysis of Survival Data 255
L. Kuo & F. Peng
1. Introduction 255
2. Likelihood 257
3. EM and Monte Carlo EM 257
4. Gibbs Sampler 259
5. Model Selection . 260
6. Example 261
6.1 EM Algorithm for the Specific Example 262
6.2 Gibbs Samplers for the Specific Example 264
6.3 Numerical Results . 265
V Model Diagnostics and Variable Selection in GLMs 271
16 Bayesian Variable Selection Using the Gibbs Sampler 273
P. Dellaportas, J. J. Forster & I. Ntzoufras
1. Introduction 273
2. Gibbs Sampler Based Variable Selection Strategies . 274
2.1 Carlin and Chib's Method 275
2.2 Stochastic Search Variable Selection 276
2.3 Unconditional Priors for Variable Selection 277
2.4 Gibbs Variable Selection 277
2.5 Summary of Variable Selection Strategies 278
3. Illustrative Example: 2x2x2 Contingency Table 278
3.1 Log-Linear models 280
3.2 Logistic Regression Models 280
4. Discussion 281
5. Appendix: BUGS CODES 282
5.1 Code for Log-linear Models for 23 Contingency Table 282
5.2 Code for Logistic Models with 2 Binary Explanatory Factors 283
17 Bayesian Methods for Variable Selection in the Cox Model 287
J. Ibrahim & M. H. Chen
1. Introduction 287
2. The Method 289
2.1 Model and Notation 289
2.2 Prior Distribution for hb(-) 289
2.3 The Likelihood Function .292
2.4 Prior Distribution for the Regression Coefficients ....... 293
2.5 Prior Distribution on the Model Space 297
3. Computational Implementation 299
3.1 Computing the Marginal Distribution of the Data 299
3.2 Sampling from the Posterior Distribution of (/3^, A) .... 302
4. Example: Simulation Study 305
5. Discussion 309
18 Bayesian Model Diagnostics for Correlated Binary Data 313
D. K. Dey & M. H. Chen
1. Introduction . 313
2. The Models 314
2.1 Stratified and Mixture Models 314
2.2 Conditional Models 314
2.3 Multivariate Probit Models ................... 315
2.4 Multivariate t-Link Models 315
3. The Prior Distributions and Posterior Computations 316
3.1 Prior Distributions 316
3.2 Posterior Computations 317
4. Model Adequacy for Correlated Binary Data 320
5. Voter Behavior Data example 324
6. Concluding Remarks 325

VI Challenging Approaches in GLMs 329
19 Bayesian Errors-in-Variables Modeling 331
J. Wukefield & D, Stephens
1. Introduction . 331
2. Illustrative Example: Case-control Study with Deprivation 333
3. Classical approaches 337
3.1 Basic Formulation 337
3.2 Modeling and Analysis: Classical Extensions and Procedures 339
4. Bayesian Approaches 339
4.1 General Framework . 339
4.2 Implementation 340
4.3 Previous Work 340
5. Example revisited 341
6. Conclusions and Discussion 342
20 Bayesian Analysis of Compositional Data 349
M. Iyengar & D. K. Dey
1. Introduction 349
2, A Parametric Approach 351
3. Simulation Based Model Determination 352
4. A Semiparametric Approach 354
5. Posterior Distributions and Estimation 355
6. Results 359
7. Conclusion 361
21 Classification Trees 365
D. G. T. Denison & В. К. Mallick
1. Introduction 365
2. The Classification Tree Model 366
2.1 The Basis Functions 366
2.2 The Classical Approach 367
2.3 The Bayesian Approach 368
3. Real data example 369
4. Discussion 371
22 Modeling and Inference for Point-Referenced Binary Spatial Data373
A. E. Gelfand, N. Ravishanker & M. Ecker
1. Introduction 373
2. Modeling Details 375
3. Computational Issues 378
4. An Illustration 380
5. Related Remarks 384
23 Bayesian Graphical Models and Software for GLMs 387
N. Best & A. Thomas
1. Bayesian Graphical Models and Conditional Independence Structures 387
1.1 Computation on Bayesian Graphical Models 388
1.2 Constructing Software from Graphical Models 389
2. Implementing GLM's Using WinBUGS 389
3. GLMs with Non-canonical Links 391
4. Generalized Linear Mixed Models (GLMMs) 391
4.1 Exchangeable Random Effects 392
4.2 Correlated Random Effects 392
5. Polytomous Responses 394
5.1 Ordered Categories 395
6. Adding Complexity in GLMs/GLMMs 396
6.1 Missing Data 396
6.2 Informative Missing Data 396
6.3 Prediction 397
6.4 Covariate Measurement Error 397
7. General Advice on Modeling Using WinBUGS 398
7.1 Parameterization 398
7.2 Prior Specification 400
7.3 Convergence and Posterior Sample Size .401
7.4 Model Checking 402
8. Extending the WinBUGS Software 402

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